qimiao si rice university
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Local Quantum Criticality and Emergent Phases. Qimiao Si Rice University. Workshop on Heavy Fermion Physics: Perspective and Outlook, Institute of Physics, CAS, Jan 8, 2012. Jed Pixley , Jianda Wu, Rong Yu (Rice University) Pallab Goswami , Seiji Yamamoto (NHMFL, FSU) - PowerPoint PPT PresentationTRANSCRIPT
Qimiao Si
Rice University
Local Quantum Criticality
and Emergent Phases
Workshop on Heavy Fermion Physics: Perspective and Outlook,
Institute of Physics, CAS, Jan 8, 2012
S. Friedemann C. Krellner Y. Tokiwa P. Gegenwart S. Paschen S. WirthN. Oeschler T. Westerkamp R. KüchlerT. Lühmann T. Cichorek K. NeumaierO. Tegus O. Trovarelli C. GeibelF. SteglichP. Coleman E. Abrahams
Jed Pixley, Jianda Wu,Rong Yu (Rice University)
Pallab Goswami, Seiji Yamamoto (NHMFL, FSU)
Stefan Kirchner (MPI-PKS,CPfS)Lijun Zhu (UC Riverside)Jian-Xin Zhu (Los Alamos)
Kevin Ingersent (U. of Florida)Jianhui Dai (Zhejiang U.)
Heavy fermions Kasahara et alO. Stockert et al
TN
Linearresistivity
Superconductivity at the Border of Magnetism
Cuprates OrganicsBroun
Faltermeier et al
Iron pnictides
YbRh2Si2
H. v. Löhneysen et al
J. Custers et al
CePd2Si2
N. Mathur et al
TN
Linearresistivity
Heavy fermion metals as prototype quantum critical points
CeCu6-xAux
“Beyond-Landau” Quantum Criticality
Inherent quantum modes, beyond order-parameter fluctuations:
-- need to identify the additional critical modes.
• Local Kondo-destruction QCP
• Global phase diagram
• Some issues and questions:– Diversity and universality of QCPs
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
• Kondo lattices:
heavy Fermi liquid:
•Kondo singlet
•Kondo resonanceNo symmetry breaking, but macroscopic order
Critical Kondo destruction (f-elec. localization)at the T=0 onset of antiferromagnetism
Critical Kondo Destruction
QS, S. Rabello, K. Ingersent & J. L. Smith, Nature 413, 804 (’01); PRB (’03)
P. Coleman et al, JPCM 13, R723 (’01)
Critical Kondo Destruction
• Extended-DMFT:
collapsing Eloc* from paramagnetic side
From the paramagnetic heavy Fermi liquid side:
• Kondo effect:
Fermi Surface Reconstruction and Energy Scales
•Kondo-destruction energy scale
•Sudden reconstruction of Fermi surface
• /T scaling in χ(q,ω,T) and G(k,ω,T)
Dynamical Scaling of Local Quantum Critical Point
= 0.72
= 0.83
= 0.78
J-X Zhu, D. Grempel and QS, PRL (2003)
J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)
M. Glossop & K. Ingersent, PRL (2007)
EDMFT: collapsing Eloc* from paramagnetic side
Dynamical Scaling of Local Quantum Critical Point
= 0.72
= 0.83
= 0.78
J-X Zhu, D. Grempel and QS, PRL (2003)
J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)
M. Glossop & K. Ingersent, PRL (2007)
EDMFT: collapsing Eloc* from paramagnetic side
Cf. neutron scattering expts: A. Schröder et al., Nature(’00);
O. Stockert et al, PRL (’98); M. Aronson et al, PRL (’95)
_
Kondo-destroying AF QCP in CeRhIn5
H. Shishido, R. Settai, H. Harima,
& Y. Onuki, JPSJ 74, 1103 (’05)
Fermi Surface and Energy Scales in YbRh2Si2
S. Friedemann, N. Oeschler, S. Wirth, C. Krellner, C. Geibel, F. Steglich, S. Paschen, S. Kirchner, and QS, PNAS 107, 14547 (2010)
S. Paschen et al, Nature (2004); P. Gegenwart et al, Science (2007)
T *
Other Approachesto Kondo Destruction
T. Senthil, M. Vojta, and S. Sachdev, PRB 69, 035111 (2004)
I. Paul, C. Pépin and M. R. Norman, PRL 98, 026402 (2007)
L. De Leo, M. Civelli and G. Kotliar, PRB 77, 075107 (2008)
P. Wölfle and E. Abrahams, PRB 84, 041101 (2011)
…
• Local Kondo-destruction QCP
• Global phase diagram
• Some issues and questions:– Diversity and universality of QCPs
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
Kondo lattice
JK<< Irkky << W
•JK=0 as the reference point of expansion:
•f- local moments: AF, QNLσM•conduction electrons: Fermi volume “x”
S. Yamamoto & QS,
PRL 99, 016401 (2007)
Heisenberg model + coherent spin path integral QNLM
Quantum non-linear Sigma Model Representation
Kondo lattice
JK<< Irkky << W
•JK=0 as the reference point of expansion:
•f- local moments: AF, QNLσM•conduction electrons: Fermi volume “x”
S. Yamamoto & QS,
PRL 99, 016401 (2007)
•JK EXACTLY MARGINAL;
•AFs “small” Fermi surface stable
JK
G
AFS
PL
AFL
I
II
Global Phase Diagram
SDW of PLQS, Physica B 378, 23 (2006)
S. Yamamoto & QS, PRL 2007
G: frustration, reduced dimensionaltiy, …
Global Phase Diagram
Q. Si, Phys. Status Solidi B247, 476 (2010)
P. Coleman & A. Nevidomskyy, JLTP 161, 182 (2010)
Global Phase Diagram
Pure and doped YbRh2Si2
S. Friedemann et al, Nat. Phys. 5, 465 (’09)
SOME ISSUES AND QUESTIONS
– Materials basis: diversity and universality
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
Global Phase Diagram
Diversity and universality of QCPs:
materials basis –
YbRh2Si2
CeCu6-xAux
CeRhIn5
CeIn3
β-YbAlB4
Ce3Pd20Si6
Yb2Pt2Pb
YbAgGe
…
Global Phase Diagram
J. Custers, K.-A. Lorenzer, M. Müller, A. Prokofiev, A. Sidorenko, H. Winkler, A.M. Strydom, Y. Shimura, T. Sakakibara, R. Yu, QS, and S.Paschen, Nature Materials (Jan. 8, 2012)
Effect of dimensionality – the case of Ce3Pd20Si6
SOME ISSUES AND QUESTIONS
– Materials basis: diversity and universality
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
Global Phase Diagram
Motivates new theoretical questions and approaches:
Global Phase Diagram
Motivates new theoretical questions and approaches:
Eg, Kondo effect fromQNLσM + Berry Phase
P. Goswami & QS, PRL 107, 126404 (’11)
More generally, how to capture Kondo effect using bosonic representations of spin
Heisenberg model + coherent spin path integral QNLM
Role of Berry Phase term in QNLσM Approach
JK<< Irkky, W
QNLσM-- chiral rotation:
Kondo effect and Berry phase in 1D
P. Goswami + QS, PRL 107,
126404 (’11)
JK<< Irkky, W
QNLσM-- chiral rotation: (Tanaka & Machida)
Kondo effect and Berry phase in 1D
Kondo vs spin-Peierls: large vs small FS in paramagnets P. Goswami + QS, PRL 107,
126404 (’11)
SOME ISSUES AND QUESTIONS
– Materials basis: diversity and universality
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
• Kondo destruction
(kicking one electron/site
out of the Fermi surface)
• What happens beyond the Kondo limit, w/ mixed-valency?
• Kondo destruction
(kicking one electron/site
out of the Fermi surface)
• What happens beyond the Kondo limit, w/ mixed-valency?
β-YbAlB4
-- H/T scaling interacting Y. Matsumoto et al, Science 331, 316
(2011)
-- Mixed valency M. Okawa et al, PRL 104, 247201 (2010)
Kondo destruction and valence fluctuations in pseudogapped asymmetric anderson model
J. Pixley, S. Kirchner, K. Ingersent and QS, arXiv:1108.5227
Charge excitations part of the quantum-critical spectrum
spin susceptibility charge susceptibility
Kondo destruction and valence fluctuations in pseudogapped asymmetric anderson model
J. Pixley, S. Kirchner, K. Ingersentand QS, arXiv:1108.5227
• Temperature dependence of valence
• Field/temperature scaling
SOME ISSUES AND QUESTIONS
– Materials basis: diversity and universality
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
T. Park et al., Nature 440, 65 (’06);
G. Knebel et al., PRB74, 020501 (’06) _
Superconductivity near Kondo-destroying AF QCP in CeRhIn5
H. Shishido, R. Settai, H. Harima,
& Y. Onuki, JPSJ 74, 1103 (’05)
T. Park et al., Nature 440, 65 (’06);
G. Knebel et al., PRB74, 020501 (’06)
Superconductivity near Kondo-destroying AF QCP in CeRhIn5
O.Stockert, J.Arndt, E.Faulhaber, C.Geibel, H.S. Jeevan, S.Kirchner,
M.Loewenhaupt, K.Schmalzl, W.Schmidt, QS, & F.Steglich, Nat. Phys. 7, 119 (2011)
Superconductivity in CeCu2Si2
Exchange energy saving≈ 20 times of SC condensation energy
large kinetic energy loss
O.Stockert, J.Arndt, E.Faulhaber, C.Geibel, H.S. Jeevan, S.Kirchner,
M.Loewenhaupt, K.Schmalzl, W.Schmidt, QS, & F.Steglich, Nat. Phys. 7, 119 (2011)
Superconductivity in CeCu2Si2
Exchange energy saving≈ 20 times of SC condensation energy
large kinetic energy loss due to transfer of spectral weight to higher energies
SUMMARY
• AF QCPs in heavy fermion metals– SDW type: Order-parameter fluctuations
– Local quantum criticality: Electronic localization
in the form of Kondo destruction
• Emergent phases:
– Global phase diagram
• Discussions and outlook:– Diversity and universality of QCPs
– Berry phase and Kondo effects
– Kondo destruction and valence fluctuations
– Implications for superconductivity
RG for mixed Bosons and Fermions with a Fermi Surface
S. Yamamoto & QS, PRB 81, 205106 (2010)
All directions scalesOnly 1 direction scales (Shankar)